Carlo Ancelotti was ousted just hours after the Italian side qualified for the last 16 of the Champions League with a 4-0 win over Belgian side Genk, amid claims of a feud with club president Aurelio De Laurentiis.
Napoli are winless in seven league games and as things stand, won't qualify for Europe.
Gattuso, who had spells with Perugia, Salernitana and AC Milan in his homeland plus a brief spell with Swiss side Sion, is expected to succeed Ancelotti at the Stadio San Paolo, according to the Daily Mail, and is set to be joined by former team-mate Riccio, who has worked alongside the 41-year-old during his coaching stints at Sion, Palermo, OFI Crete in Greece, Pisa - who they took to Serie B - and AC Milan.
Pressure to deliver
The pair are expected to be offered six-month contracts, with an extra 12 months if they deliver certain results, such as qualifying for European football's premier club competition. Napoli currently lie in seventh place in Serie A, eight points adrift of Cagliari who currently occupy the last Champions League berth.
Ricco signed for Rangers at the same time as Gattuso in 1998 but made just one substitute appearance during a match with Motherwell in May 1999. He was an unused sub when the Ibrox side famously won the league at Celtic Park later that month and is better known for his seven-year stint at Piacenza, and two seasons with Sassuolo before hanging up his boots in 2009.
According to reports, Ancelotti has already spoken with Gattuso on the phone to wish him luck in the new post. The 73-cap Italian international has a close relationship with the 60-year-old manager, whom he played under at the San Siro.
The Reggiolo-born boss is now on the lookout for a new club, having served as manager of Reggiana, Parma, Juventus, AC Milan, Chelsea, Paris Saint-Germain and Bayern Munich as well as Napoli.